Peter and Mary want to buy identical GT2 911s in 7 years, to establish bragging rights at the Nordschleife. Paul will buy a Huracan, but wisely isn't going to bother showing up. The GT2 costs $327,000 today which is expected to increase at an annualrate of 3% per year. Both will invest a single amount today in accounts that pay 8.1% APR, but Peter's account compounds monthly,and Mary's semiannually. How much more must Mary invest compared to Peter? Round your final answer to the nearest whole dollar and leave out the "$" sign.
| 1] | Price of the GT2 in 7 years after accounting for escalation in price = 327000*1.03^7 = | $ 402,169 |
| 2] | Amount to be deposited today by Peter [with monthly compounding] = 402169/(1+0.081/12)^84 = | $ 228,555 |
| 3] | Amount to be deposited today by Mary [with semi-annual compounding] = 402169/(1+0.081/2)^14 = | $ 230,685 |
| Additional investment to be made by Mary = 230685-228555 = | $ 2,130 |
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